Advancements in disciplines ranging from atomic physics to various branches of condensed matter physics are being employed to fabricate a variety of different diamond-based materials that can be used in many different technological applications. Diamond has a crystal-lattice structure comprising two interpenetrating face-centered cubic lattices of carbon atoms. FIG. 1 shows a unit cell 100 of a diamond-crystal lattice. In FIG. 1, each carbon atom, represented by a sphere, is covalently bonded to four adjacent carbon atoms, each covalent bond is represented by a rod connecting two spheres. As shown in FIG. 1, a carbon atom 102 is covalently bonded to four carbon atoms 103-106. In general, diamond has a number of potentially useful properties. For example, diamond is transparent from the ultraviolet to the far infrared of the electromagnetic spectrum and has a relatively high refractive index of about 2.42. Diamond may also be a suitable replacement for silicon in semiconductor devices. For example, silicon has an electronic bandgap of about 1.12 eV and starts to show signs of thermal stress at about 100° Celsius, while diamond has a larger electronic bandgap ranging from about 5 eV to about 7 eV and a higher Debye temperature ranging from about 1550° Celsius to about 1930° Celsius.
Diamond may have certain crystal defects, called “color centers,” that have potential applications in quantum computing and quantum information processing. For example, a nitrogen-vacancy (“NV”) center embedded in diamond is a type of color center that may be used to store a quantum bit of information. FIG. 2 shows an NV center embedded in a diamond-crystal lattice 200. The NV center comprises a nitrogen atom 202, substituted for a carbon atom, next to a vacancy 204 in the carbon lattice. The nitrogen atom 202 is covalently bonded to three carbon atoms 206-208. NV centers can be created in nitrogen-containing diamond by irradiation and subsequent annealing at temperatures above 550° C. The radiation creates vacancies in the diamond and subsequent annealing causes the vacancies to migrate towards nitrogen atoms to produce NV centers. Alternatively, NV centers can be created in diamond using N+ ion implantation.
When an electromagnetic field interacts with an NV center, there is a periodic exchange, or oscillation, of energy between the electromagnetic field and the electronic energy levels of the NV center. Such oscillations, which are called “Rabi oscillations,” are associated with oscillations of the NV center electronic energy level populations and quantum-mechanical probability amplitudes of the NV center electronic energy states. Rabi oscillations can be interpreted as an oscillation between absorption and stimulated emission of photons. The Rabi frequency, denoted by Ω, represents the number of times these oscillations occur per unit time.
FIG. 3 illustrates an energy-level diagram of electronic states of a negatively charged NV center. Under applied stress or an electric field, the E3 excited states, which have an optical doublet, spin triplet structure, split into upper and lower branches with different orbital states. Only the lower branch of the excited states, consisting of three spin levels, is shown in the FIG. 3. Normally, the optical transitions are spin converging. However, when the orbital splitting induced by the applied stress or electric field is in a range from about 15 GHz to about 45 GHz, the spin-orbit interaction can mix the excited states so that spin-non-conserving transitions are allowed. In this case, it may be possible to obtain Λ-type configuration comprising multiple ground states coupled to a common excited state. The three ground 3A2 states comprise a first ground state |1 with a lowest energy level 300, and a pair of nearly degenerate ground states |2 and |3 with energy levels 302 and 304, respectively. In FIG. 3, all three ground states are coupled to an excited state 306, labeled |4. The three double-headed directional arrows 308-310, correspond to optical transitions that may be driven by two laser frequencies. A first laser drives the |1→|4 transition, while a second laser drives both the |2→|4 and the |3→|4 transitions. A parameter δ1 represents the laser frequency detuning for a |1→|4 transition, a parameter δ2 is the laser frequency detuning for a |2→|4 transition, and a parameter δ23 is the |2⇄|3 energy splitting. When δ1=δ2 or δ1=δ2+δ3, the system will relax through spontaneous emission into stable “dark” states, which are linear combinations of the states |1, |2, and |3, with probability amplitudes that are tunable through the laser amplitudes. These dark resonance states can be used, for example, for all-optical manipulation of the electron spin. Note that the exact structure of the 3E state depends on the strain or other mechanical effects exerted on the diamond crystal. Also, the excited-state linewidths depend on the temperature. In order to obtain optical linewidths that are less than 100 MHz, the temperature of the diamond crystal is usually lowered to a temperature below 20K. With narrow optical linewidths, it is possible to manipulate the spins of single NV centers using the optical transitions shown in FIG. 3.
The NV centers are appealing for quantum information processing because the NV center has a relatively long-lived spin coherence time and a possibility of large-scale integration into diamond structures using semiconductor processing technology. For example, an NV center has been observed to have an electron spin coherence time of 58 μm at room temperature and much longer electron spin coherence times have been observed at temperatures below room temperature. NV centers may have relatively long-lived spin coherence because the lattice comprises primarily 12C, which has zero nuclear spin. In addition, a single photon can be generated from an NV center at room temperature, which has established NV centers as potential photon sources for quantum cryptography.
However, it is difficult to control the precise location of the NV centers in diamond using conventional fabrication techniques, such as ion implantation or irradiation of nitrogen-containing diamond. In order to take advantage of the unusual electronic and optical properties of NV centers for photonic devices, it is important to be able to accurately position the NV centers. Therefore, manufacturers and designers of photonic devices can appreciate a need for being able to accurately position color centers in diamond or other optical media in order to fabricate useful photonic devices.